Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Dahmen, Sander R."'
Number fields and their rings of integers, which generalize the rational numbers and the integers, are foundational objects in number theory. There are several computer algebra systems and databases concerned with the computational aspects of these.
Externí odkaz:
http://arxiv.org/abs/2409.18030
Autor:
Dahmen, Sander R., van Langen, Joey M.
In this paper we consider elliptic divisibility sequences generated by a point on an elliptic curve over $\mathbb{Q}$ with $j$-invariant $1728$ given by an integral short Weierstrass equation. For several different such elliptic divisibility sequence
Externí odkaz:
http://arxiv.org/abs/2310.13244
Diophantine equations are a popular and active area of research in number theory. In this paper we consider Mordell equations, which are of the form $y^2=x^3+d$, where $d$ is a (given) nonzero integer number and all solutions in integers $x$ and $y$
Externí odkaz:
http://arxiv.org/abs/2209.15492
Dedekind domains and their class groups are notions in commutative algebra that are essential in algebraic number theory. We formalized these structures and several fundamental properties, including number theoretic finiteness results for class group
Externí odkaz:
http://arxiv.org/abs/2102.02600
In 2016, Ellenberg and Gijswijt established a new upper bound on the size of subsets of $\mathbb{F}^n_q$ with no three-term arithmetic progression. This problem has received much mathematical attention, particularly in the case $q = 3$, where it is c
Externí odkaz:
http://arxiv.org/abs/1907.01449
Publikováno v:
Math. Proc. Camb. Phil. Soc. 158 (2015) 305-329
Let $u_k$ be a Lucas sequence. A standard technique for determining the perfect powers in the sequence $u_k$ combines bounds coming from linear forms in logarithms with local information obtained via Frey curves and modularity. The key to this approa
Externí odkaz:
http://arxiv.org/abs/1408.1710
Autor:
Dahmen, Sander R., Siksek, Samir
We show that the generalized Fermat equations with signatures (5,5,7), (5,5,19), and (7,7,5) (and unit coefficients) have no non-trivial primitive integer solutions. Assuming GRH, we also prove the nonexistence of non-trivial primitive integer soluti
Externí odkaz:
http://arxiv.org/abs/1309.4030
Autor:
Dahmen, Sander R., Yazdani, Soroosh
Publikováno v:
Can. J. Math.-J. Can. Math. 64 (2012) 282-300
We discuss a clean level lowering theorem modulo prime powers for weight $2$ cusp forms. Furthermore, we illustrate how this can be used to completely solve certain twisted Fermat equations $ax^n+by^n+cz^n=0$.
Externí odkaz:
http://arxiv.org/abs/1009.0284
Autor:
Dahmen, Sander R.
Let $n$ be a positive integer and consider the Diophantine equation of generalized Fermat type $x^2+y^{2n}=z^3$ in nonzero coprime integer unknowns $x,y,z$. Using methods of modular forms and Galois representations for approaching Diophantine equatio
Externí odkaz:
http://arxiv.org/abs/1002.0020
Autor:
Bruin, Nils, Dahmen, Sander R.
Publikováno v:
Algorithmic Number Theory Lecture Notes in Computer Science, 2010, Volume 6197/2010, 110-125
Mazur proved that any element xi of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in the sense that xi lies in the kernel of the natural homomorphism between the coh
Externí odkaz:
http://arxiv.org/abs/1001.5302